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COLUMBUS, Ohio — Two Ohio teenagers on a school mission trip to Costa Rica died in the Pacific Ocean when they were pulled along by an undertow current, and a third student swept out with them has not been found, officials said yesterday.

The three were spending an afternoon at the beach when Wednesday’s accident occurred, according to a statement from Patriot Preparatory Academy in Columbus. They were among eight members of the junior and senior classes who were on a service trip in the Central American country and were to return home yesterday, the school said.

The first body recovered was that of Caity Jones. James Smith’s body was recovered yesterday, and authorities were still searching for missing student, Kai Lamar, said Freddy Roman, a Red Cross spokesman.

Members of The Redeemer’s on Courtright Church in Columbus, where Smith and his family attend, had been praying for good news, said associate pastor Rick Kulich.

He described Smith as a “brainiac’’ who looked younger than his 16 years.

“He wanted to be a servant in the sense of working with the youth pastor and the youth leaders, just a good-hearted kid,’’ Kulich said.

The boy’s father and the church’s pastor, Dwight Bennett, were trying to make their way to Costa Rica together yesterday, the associate pastor said.

The three teens were swept out by a rip current in the Pacific near the town of Parrita, the Costa Rican Red Cross told the Tico Times newspaper. They were doing missionary work at an orphanage and a drug rehabilitation center, among other places, according to a blog the group is keeping on the trip.

A visit to the orphanage “was one of the most touching things I had ever seen,’’ one of the students blogged.